Diffusion effects Nemst

Since the separation between the tip and the surface is such that their respective double layers do not overlap, the nanostmcturing process can be described simply through the diffusion of the ions toward the surface. Thus, the concentration profiles of the diffusing ions dehne effective Nemst potential prohles that can be employed to predict the regions where the oversaturation conditions will contribute to metal nucleation and growth. 

The electrodeposition process is complicated, but can be simply thought of as the transfer of ions to and/or from the metal surface [58], It is well known that when a metal is immersed in an aqueous solution a diffusion layer (Nemst diffusion layer) forms at the metal/solution interface. If an electrochemical reaction is to occur at the metal surface it is therefore necessary for ions to be transported across this diffusion layer. Any process which can affect this layer will therefore influence the electrochemical process. Ultrasound is known to reduce the thickness of this diffusion layer [26] but is unlikely to completely remove it as was suggested by early Russian workers. Ultrasound can also effect electrochemical reactions since it produces surface cavitation and acoustic streaming both of which assist diffusion to and from the metal surface, this movement often being the rate-controlling step in electrochemical processes such as deposition. 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

The EMD studies are performed without any external electric field. The applicability of the EMD results to useful situations is based on the validity of the Nemst-Planck equation, Eq. (10). From Eq. (10), the current can be computed from the diffusion coefficient obtained from EMD simulations. It is well known that Eq. (10) is valid only for a dilute concentration of ions, in the absence of significant ion-ion interactions, and a macroscopic theory can apply. Intuitively, the Nemst-Planck theory can be expected to fail when there is a significant confinement effect or ion-wall interaction and at high electric... 

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

The diffusion flux J, in mol/cm, is proportional to the concentration gradient and inversely proportional to the diffusion layer s effective thickness 5 (also called the Nemst thickness). The proportionality constant D is the diffusion constant hence,... 

For inter diffusion between same-valence ions (ionic exchange) in an aqueous solution, or a melt, or a solid solution such as olivine (Fe +, Mg +)2Si04, an equation similar to Equation 3-135c has been derived from the Nemst-Planck equations first by Helfferich and Plesset (1958) and then with refinement by Barter et al. (1963) with the assumption that (i) the matrix (or solvent) concentration does not vary and (ii) cross-coefficient Lab (phenomenological coefficient in Equation 3-96a) is negligible, which is similar to the activity-based effective binary diffusion treatment. The equation takes the following form ... 

When a biocatalyst is immobilized on or within a solid matrix, mass transfer effects may exist because the substrate must diffuse from the bulk solution to the immobilized biocatalyst. If the biocatalyst is attached to non-porous supports there are only external mass transfer effects on the catalytically active outer surface in the reaction solution, the supports are surrounded by a stagnant film and substrate and product are transported across this Nemst layer by diffusion. The driving force for this diffusion is the concentration difference between the surface and the bulk concentration of substrate and product. 

Voltammetry. Diffusional effects, as embodied in equation 1, can be avoided by simply stirring the solution or rotating the electrode, eg, using the rotating disk electrode (RDE) at high rpm (3,7). The resultant concentration profiles then appear as shown in Figure 5. A time-independent Nemst diffusion layer having a thickness dictated by the laws of hydrodynamics is established. For the RDE,... 

Another example for the HMRRD electrode is given in Fig. 9 for Fe in alkaline solutions [12, 27]. The square wave modulation of the rotation frequency co causes the simultaneous oscillation of the analytical ring currents. They are caused by species of the bulk solution. Additional spikes refer to corrosion products dissolved at the Fe disc. This is a consequence of the change of the Nemst diffusion layer due to the changes of co. This pumping effect leads to transient analytical ring currents. Besides qualitative information, also quantitative information on soluble corrosion products may be obtained. The size of the spikes is proportional to the dissolution rate at the disc, as has been shown by a close relation of experimental results and calculations [28-30]. As seen in Fig. 7, soluble Fe(II) species are formed in the po-... 

On dissociation of a salt, ions start to diffuse in a solution. Without an electric potential effect, however, the diffusion of a single salt is treated as molecular diffusion. For dilute solutions of a salt, the Nemst-Haskell equation is used to estimate the dilfusivity coefficient... 

Relaxed interfaces cannot be polarized unless special precautions are taken. Capacitances can of course be obtained as derived quantities by differentiating the surface charge with respect to the surface potentieil if changes In the latter are known, which is possible if the Nemst equation applies. We now discuss direct capacitance measurements on reversible interfaces. To start with, the response of such an interface to an applied field has to be considered. The basic problem is that not only are double layers built up, but also charge transfer across the interfaces takes place and diffusion of charge-determining ions to or from the surface starts to play a role. With regard to these physical processes only the sum-effect is measured, and this sum has to be divided into its parts to obtain the capacitance. Distinctions can be made because the three constituents mentioned react in a different way to the frequency of the external field. 

Flow along uncharged surfaces has been considered in secs. I.6.4f and e. surface conduction in sec. I.6.6d and mixed transport phenomena, simultaneously involving electrical, mechanical and diffusion types of transport In sec. 1.6.7. Specifically the Nemst-Planck equation ((1.6.7.1 or 2]) is recalled, formulating ion fluxes caused by the sum-effect of diffusion, conduction and convection. 

Moreover the electrodiffusion potential gradient is likely to cause electroosmotic transfer of the solution, whose local content is not in equilibrium with that of the counterions [5]. In this case, as it is pointed out in Ref. 5, the ion mobility and concentration depend on the prior history of the process which can bring about non-Fickian diffusion. The application of Nemst-Planck equations to the real system may require inclusion of additional terms that account for the effect of activity coefficient gradients which may be important in IE with zeolites [4,5]. 

Within the Nemst hypothesis, the diffusion impedance is assumed to be that for a stagnant film of effective thickness that is related to velocity by... 

The diffusion (Ed), thermal diffusion (Etd)> thermoelectric ( te)> and streaming (2 str) potentials are the potentials that are not desirable in the potentiomet-ric measurements but can occur. If these phenomena have an effect, they should be taken into account to correctly translate the measured open-circuit potential to thermodynamic properties of the electrochemical system using a generalized Nemst equation ... 

Kinetics of ion exchange is usually considered to be controlled by mass transfer in ion exchange particles or in the immediately surrounding liquid phase. The theory used to describe mass transfer in the particle is based on the Nemst-Planck equations developed by Helffericht which accounted for the effect of the electric field generated by ionic diffusion, but excluded convection. 

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